Mister Exam

# Factor polynomial y^5+y^3+y^2+1

An expression to simplify:

### The solution

You have entered [src]
 5    3    2
y  + y  + y  + 1
$$\left(y^{2} + \left(y^{5} + y^{3}\right)\right) + 1$$
y^5 + y^3 + y^2 + 1
Factorization [src]
                        /              ___\ /              ___\
|      1   I*\/ 3 | |      1   I*\/ 3 |
(x + 1)*(x + I)*(x - I)*|x + - - + -------|*|x + - - - -------|
\      2      2   / \      2      2   /
$$\left(x + 1\right) \left(x + i\right) \left(x - i\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right)$$
((((x + 1)*(x + i))*(x - i))*(x - 1/2 + i*sqrt(3)/2))*(x - 1/2 - i*sqrt(3)/2)
General simplification [src]
     2    3    5
1 + y  + y  + y 
$$y^{5} + y^{3} + y^{2} + 1$$
1 + y^2 + y^3 + y^5
Combining rational expressions [src]
     2 /      /     2\\
1 + y *\1 + y*\1 + y //
$$y^{2} \left(y \left(y^{2} + 1\right) + 1\right) + 1$$
1 + y^2*(1 + y*(1 + y^2))
Assemble expression [src]
     2    3    5
1 + y  + y  + y 
$$y^{5} + y^{3} + y^{2} + 1$$
1 + y^2 + y^3 + y^5
Powers [src]
     2    3    5
1 + y  + y  + y 
$$y^{5} + y^{3} + y^{2} + 1$$
1 + y^2 + y^3 + y^5
1.0 + y^2 + y^3 + y^5
1.0 + y^2 + y^3 + y^5
Combinatorics [src]
        /     2\ /     2    \
(1 + y)*\1 + y /*\1 + y  - y/
$$\left(y + 1\right) \left(y^{2} + 1\right) \left(y^{2} - y + 1\right)$$
(1 + y)*(1 + y^2)*(1 + y^2 - y)
Trigonometric part [src]
     2    3    5
1 + y  + y  + y 
$$y^{5} + y^{3} + y^{2} + 1$$
1 + y^2 + y^3 + y^5
Common denominator [src]
     2    3    5
1 + y  + y  + y 
$$y^{5} + y^{3} + y^{2} + 1$$
1 + y^2 + y^3 + y^5
Rational denominator [src]
     2    3    5
1 + y  + y  + y 
$$y^{5} + y^{3} + y^{2} + 1$$
1 + y^2 + y^3 + y^5